A266837 Triangle read by rows giving successive states of cellular automaton generated by "Rule 67" initiated with a single ON (black) cell.

1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1

Offset

0

Comments

Row n has length 2n+1.

Links

Robert Price, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Example

The first ten rows:
                  1
                1 0 0
              0 1 0 1 0
            1 1 0 0 0 0 1
          0 0 1 0 1 1 1 0 0
        1 1 1 0 0 0 0 1 0 1 1
      0 0 0 1 0 1 1 1 0 0 0 0 0
    1 1 1 1 0 0 0 0 1 0 1 1 1 1 1
  0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0
1 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1

Mathematica

rule=67; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Flatten[catri] (* Triangle Representation of CA *)

Crossrefs

Cf. A266838, A266839, A266441 (rows reversed).

Sequence in context: A327580 A163811 A163817 * A321081 A267126 A373991

Adjacent sequences: A266834 A266835 A266836 * A266838 A266839 A266840

Keyword

nonn,tabf,easy,changed

Author

Robert Price, Jan 04 2016

Status

approved